What is the range of f(x)=-5t^2+10t-3 ?

The range of f(x)=-5t^2+10t-3 is f(x)<= 2

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range of f(x)=-5t^2+10t-3

range

f (x) = - 5 t^{2} + 10 t - 3

f (x) \leq 2

Interval Notation

(- \infty, 2]

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

- 5 t^{2} + 10 t - 3

Inverse of

- 5 t^{2} + 10 t - 3 : - \frac{- 10 + - 20 t + 40}{10}, - \frac{- 10 - - 20 t + 40}{10}

- \frac{- 10 + - 20 t + 40}{10}, - \frac{- 10 - - 20 t + 40}{10}

Find the domain of each inverse function

Domain of

- \frac{- 10 + - 20 t + 40}{10} : t \leq 2

Domain of

- \frac{- 10 - - 20 t + 40}{10} : t \leq 2

Combine the intervals

f (x) \leq 2

What is the range of f(x)=-5t^2+10t-3 ?
The range of f(x)=-5t^2+10t-3 is f(x)<= 2